. 2022 Mar 1;191(8):1485–1495. doi: 10.1093/aje/kwac035

Table 7.

Example of Incomplete Confounding Adjustment and Spurious Effect Modification on the Relative Scale Due to Covariate Misclassification

	Outcome Status (n)		Total (n)	Risk ^a	RR	Adjusted RR (SMR)
Data Set	D+	D−	Total (n)	Risk ^a	RR	Adjusted RR (SMR)
Correctly Classified Data
Total						0.70
E+	60	270	330	0.18	1.23
E−	130	750	880	0.15	1.00^b
C+
E+	45	70	115	0.39	0.70
E−	50	40	90	0.56	1.00^b
C−
E+	15	200	215	0.07	0.69
E−	80	710	790	0.10	1.00^b
Covariate Misclassified With 80% Specificity and 70% Sensitivity ^c
Total						1.13
E+	60	270	330	0.18	1.23
E−	130	750	880	0.15	1.00^b
C+
E+	34.5	89	123.5	0.28	1.21
E−	51	170	221	0.23	1.00^b
C−
E+	25.5	181	206.5	0.12	1.03
E−	79	580	659	0.12	1.00^b

Abbreviations: RR, risk ratio; SMR, standardized mortality ratio.

^a Risk = number in D+/total number.

^b Referent.

^c Misclassification of the confounder, C, is nondifferential with respect to both the exposure and the outcome, with 80% specificity and 70% sensitivity. In this example, the true unbiased RR is 0.70, the crude RR is 1.23, and the RR adjusted for the misclassified variable C is 1.13. While there is no evidence of effect modification on the relative scale in the correctly classified data, the stratum-specific RRs in the misclassified data are 1.03 and 1.21, falsely suggesting effect modification by C.